What is the solution for y^{''}-2y^'-35y=768e^{-t} ?

The solution for y^{''}-2y^'-35y=768e^{-t} is y=c_{1}e^{7t}+c_{2}e^{-5t}-24e^{-t}

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y^{''}-2y^'-35y=768e^{-t}

y^{^{''}} - 2 y^{^{'}} - 35 y = 768 e^{- t}

y = c_{1} e^{7 t} + c_{2} e^{- 5 t} - 24 e^{- t}

Solution steps

y^{''} (t) - 2 y^{'} (t) - 35 y = 768 e^{- t}

Solve linear ODE:

y = c_{1} e^{7 t} + c_{2} e^{- 5 t} - 24 e^{- t}

y = c_{1} e^{7 t} + c_{2} e^{- 5 t} - 24 e^{- t}

y^{^{''}} - y^{^{'}} - 6 y = - e^{x} + 12

y^{^{''}} + 4 y = sec (22 x)

y^{^{''''}} - 2 y^{^{''}} + y = e^{x}

\frac{d ^{2} y}{d x ^{2}} + y = (sec (x))^{3}

y^{^{''}} - 2 y^{^{'}} - 3 y = 2 e^{5 t}

What is the solution for y^{''}-2y^'-35y=768e^{-t} ?
The solution for y^{''}-2y^'-35y=768e^{-t} is y=c_{1}e^{7t}+c_{2}e^{-5t}-24e^{-t}